Thread Subject: Create a curve surface

Hi,
I wan to to create a curved surface with a curvature of 20 degree on
either sides from the center in the horizontal plane and a
corresponding
curvature in vertical direction. In other words I want to use
surf(Z) , where Z is of 30x20 grid if plotted gives a curved surface
and not a flat surface. Since the grid is unequal therefore the
curvature in vertical direction will automatically decrease. It would
be same if I use 30x30 grid (which I do not want). Any ideas ?

In article <d2c57973-9b2e-45f9-a521-e0f45d6d5d24@c19g2000prf.googlegroups.com>, fas <faisalmufti@gmail.com> wrote:

> Hi,
> I wan to to create a curved surface with a curvature of 20 degree on
> either sides from the center in the horizontal plane and a
> corresponding
> curvature in vertical direction. In other words I want to use
> surf(Z) , where Z is of 30x20 grid if plotted gives a curved surface
> and not a flat surface. Since the grid is unequal therefore the
> curvature in vertical direction will automatically decrease. It would
> be same if I use 30x30 grid (which I do not want). Any ideas ?

I'm confused. Curvature would not be
described in terms of degrees.

You will probably need to define your
surface parametrically, and perhaps as
a piecewise thing. I'm just guessing
because I really have no idea what you
are trying to describe.

John


--
The best material model of a cat is another, or preferably the same, cat.
A. Rosenblueth, Philosophy of Science, 1945

Those who can't laugh at themselves leave the job to others.
Anonymous

On May 29, 6:54 am, John D'Errico <woodch...@rochester.rr.com> wrote:
> In article <d2c57973-9b2e-45f9-a521-e0f45d6d5...@c19g2000prf.googlegroups.com>, fas <faisalmu...@gmail.com> wrote:
>
> > Hi,
> > I wan to to create a curved surface with a curvature of 20 degree on
> > either sides from the center in the horizontal plane and a
> > corresponding
> > curvature in vertical direction. In other words I want to use
> > surf(Z) , where Z is of 30x20 grid if plotted gives a curved surface
> > and not a flat surface. Since the grid is unequal therefore the
> > curvature in vertical direction will automatically decrease. It would
> > be same if I use 30x30 grid (which I do not want). Any ideas ?
>
> I'm confused. Curvature would not be
> described in terms of degrees.
>
> You will probably need to define your
> surface parametrically, and perhaps as
> a piecewise thing. I'm just guessing
> because I really have no idea what you
> are trying to describe.
>
> John
>
> --
> The best material model of a cat is another, or preferably the same, cat.
> A. Rosenblueth, Philosophy of Science, 1945
>
> Those who can't laugh at themselves leave the job to others.
> Anonymous

Ok, imagine if I have a grid of 30x30 and I want to bend it. The angle
of bend is measured from the center of the grid. So the center point
have a zero bend. Continuing in this way the edges will have the
maximum bend (say 25 degrees)

Now the second step that not only it should have a bend side wise of
25 degrees on either sides from the center but also a bend vertically
as well of some 15 degrees.

It is just if you have a metal sheet and you want to bend it. Imagine
a 30x30 mesh grid as metal sheet.

On May 29, 10:04 am, fas <faisalmu...@gmail.com> wrote:
> On May 29, 6:54 am, John D'Errico <woodch...@rochester.rr.com> wrote:
>
>
>
> > In article <d2c57973-9b2e-45f9-a521-e0f45d6d5...@c19g2000prf.googlegroups.com>, fas <faisalmu...@gmail.com> wrote:
>
> > > Hi,
> > > I wan to to create a curved surface with a curvature of 20 degree on
> > > either sides from the center in the horizontal plane and a
> > > corresponding
> > > curvature in vertical direction. In other words I want to use
> > > surf(Z) , where Z is of 30x20 grid if plotted gives a curved surface
> > > and not a flat surface. Since the grid is unequal therefore the
> > > curvature in vertical direction will automatically decrease. It would
> > > be same if I use 30x30 grid (which I do not want). Any ideas ?
>
> > I'm confused. Curvature would not be
> > described in terms of degrees.
>
> > You will probably need to define your
> > surface parametrically, and perhaps as
> > a piecewise thing. I'm just guessing
> > because I really have no idea what you
> > are trying to describe.
>
> > John
>
> > --
> > The best material model of a cat is another, or preferably the same, cat.
> > A. Rosenblueth, Philosophy of Science, 1945
>
> > Those who can't laugh at themselves leave the job to others.
> > Anonymous
>
> Ok, imagine if I have a grid of 30x30 and I want to bend it. The angle
> of bend is measured from the center of the grid. So the center point
> have a zero bend. Continuing in this way the edges will have the
> maximum bend (say 25 degrees)
>
> Now the second step that not only it should have a bend side wise of
> 25 degrees on either sides from the center but also a bend vertically
> as well of some 15 degrees.
>
> It is just if you have a metal sheet and you want to bend it. Imagine
> a 30x30 mesh grid as metal sheet.

I have tried this
[x,y]=meshgrid(-15:15,-15:15);
r=sqrt(x.^2+y.^2);
rs=(r./sum(sum(r)));
figure, surf(cos(ra))
But it does not curve with the angles I want :(

fas <faisalmufti@gmail.com> wrote in message <7252ddf3-be6d-47f6-
a11d-5b6e9608242e@v26g2000prm.googlegroups.com>...

> Ok, imagine if I have a grid of 30x30 and I want to bend it. The angle
> of bend is measured from the center of the grid. So the center point
> have a zero bend. Continuing in this way the edges will have the
> maximum bend (say 25 degrees)
>
> Now the second step that not only it should have a bend side wise of
> 25 degrees on either sides from the center but also a bend vertically
> as well of some 15 degrees.
>
> It is just if you have a metal sheet and you want to bend it. Imagine
> a 30x30 mesh grid as metal sheet.

You have not yet made a good enough
description of the shape, and the shape
of this doubly curved sheet, at least not
to build the shape as a parametric
surface of some form.

Were I to do this, I might set it up as a
deformed, flexible sheet, using a finite
element approximation. Fix the position
of the center of the sheet. Then fix the
slope of the sheet along the edges, and
solve the system of equations that will
define the final shape of the sheet. You
would need to deal with both the potential
energy of bending in the plate, as well
as the energy due to in-plane strains
because of the dually curved plate.

The above analysis will probably be more
than you really want to do. A simple
alternative might be to consider this as
the super-position of two deformations.

Assume the form is a segment of a
cylinder, curved in x and z. Then add
a second deformation, defined in the
y-z directions. The super-position of
these two will give something perhaps
like what you want.

As an example, I'll build a 31x31 grid.

[x0,y0] = meshgrid(-15:15);
z0 = zeros(size(x0));

dx1 = -5*sin(x0*(pi/3/15));
dz1 = 5*cos(x0*(pi/3/15));
dy1 = zeros(size(x0));

dy2 = -4*sin(y0*(pi/4/15));
dz2 = -4*cos(y0*(pi/4/15));
dx2 = zeros(size(x0));

xfinal = x0 + dx1 + dx2;
yfinal = y0 + dy1 + dy2;
zfinal = z0 + dz1 + dz2;

surf(xfinal,yfinal,zfinal)
camlight right
lighting phong
shading interp
box on
grid on

I'll let you figure out the proper set of
parameters.

John

On May 29, 12:11 pm, "John D'Errico" <woodch...@rochester.rr.com>
wrote:
> fas <faisalmu...@gmail.com> wrote in message <7252ddf3-be6d-47f6-
>
> a11d-5b6e96082...@v26g2000prm.googlegroups.com>...
>
> > Ok, imagine if I have a grid of 30x30 and I want to bend it. The angle
> > of bend is measured from the center of the grid. So the center point
> > have a zero bend. Continuing in this way the edges will have the
> > maximum bend (say 25 degrees)
>
> > Now the second step that not only it should have a bend side wise of
> > 25 degrees on either sides from the center but also a bend vertically
> > as well of some 15 degrees.
>
> > It is just if you have a metal sheet and you want to bend it. Imagine
> > a 30x30 mesh grid as metal sheet.
>
> You have not yet made a good enough
> description of the shape, and the shape
> of this doubly curved sheet, at least not
> to build the shape as a parametric
> surface of some form.
>
> Were I to do this, I might set it up as a
> deformed, flexible sheet, using a finite
> element approximation. Fix the position
> of the center of the sheet. Then fix the
> slope of the sheet along the edges, and
> solve the system of equations that will
> define the final shape of the sheet. You
> would need to deal with both the potential
> energy of bending in the plate, as well
> as the energy due to in-plane strains
> because of the dually curved plate.
>
> The above analysis will probably be more
> than you really want to do. A simple
> alternative might be to consider this as
> the super-position of two deformations.
>
> Assume the form is a segment of a
> cylinder, curved in x and z. Then add
> a second deformation, defined in the
> y-z directions. The super-position of
> these two will give something perhaps
> like what you want.
>
> As an example, I'll build a 31x31 grid.
>
> [x0,y0] = meshgrid(-15:15);
> z0 = zeros(size(x0));
>
> dx1 = -5*sin(x0*(pi/3/15));
> dz1 = 5*cos(x0*(pi/3/15));
> dy1 = zeros(size(x0));
>
> dy2 = -4*sin(y0*(pi/4/15));
> dz2 = -4*cos(y0*(pi/4/15));
> dx2 = zeros(size(x0));
>
> xfinal = x0 + dx1 + dx2;
> yfinal = y0 + dy1 + dy2;
> zfinal = z0 + dz1 + dz2;
>
> surf(xfinal,yfinal,zfinal)
> camlight right
> lighting phong
> shading interp
> box on
> grid on
>
> I'll let you figure out the proper set of
> parameters.
>
> John

What I have done is this
angle=25;
x = angle*(-pi/180):0.1:angle*(pi/180); y = angle*(-pi/180):
0.1:angle*(pi/180);
[xIndex, yIndex] = meshgrid(x, y);
v = sqrt(xIndex.^2 + yIndex.^2);
surf(cos(v))
Now I need to run cos(v) not from 32x32 but 40x20 and have the values
scaled according to it. Such that along x dimension the angle runs
between 25 degree and along Y with corresponding angle ( will be less
then 25 degree I believe)
any suggestions ?

On May 29, 1:55 pm, fas <faisalmu...@gmail.com> wrote:
> On May 29, 12:11 pm, "John D'Errico" <woodch...@rochester.rr.com>
> wrote:
>
>
>
> > fas <faisalmu...@gmail.com> wrote in message <7252ddf3-be6d-47f6-
>
> > a11d-5b6e96082...@v26g2000prm.googlegroups.com>...
>
> > > Ok, imagine if I have a grid of 30x30 and I want to bend it. The angle
> > > of bend is measured from the center of the grid. So the center point
> > > have a zero bend. Continuing in this way the edges will have the
> > > maximum bend (say 25 degrees)
>
> > > Now the second step that not only it should have a bend side wise of
> > > 25 degrees on either sides from the center but also a bend vertically
> > > as well of some 15 degrees.
>
> > > It is just if you have a metal sheet and you want to bend it. Imagine
> > > a 30x30 mesh grid as metal sheet.
>
> > You have not yet made a good enough
> > description of the shape, and the shape
> > of this doubly curved sheet, at least not
> > to build the shape as a parametric
> > surface of some form.
>
> > Were I to do this, I might set it up as a
> > deformed, flexible sheet, using a finite
> > element approximation. Fix the position
> > of the center of the sheet. Then fix the
> > slope of the sheet along the edges, and
> > solve the system of equations that will
> > define the final shape of the sheet. You
> > would need to deal with both the potential
> > energy of bending in the plate, as well
> > as the energy due to in-plane strains
> > because of the dually curved plate.
>
> > The above analysis will probably be more
> > than you really want to do. A simple
> > alternative might be to consider this as
> > the super-position of two deformations.
>
> > Assume the form is a segment of a
> > cylinder, curved in x and z. Then add
> > a second deformation, defined in the
> > y-z directions. The super-position of
> > these two will give something perhaps
> > like what you want.
>
> > As an example, I'll build a 31x31 grid.
>
> > [x0,y0] = meshgrid(-15:15);
> > z0 = zeros(size(x0));
>
> > dx1 = -5*sin(x0*(pi/3/15));
> > dz1 = 5*cos(x0*(pi/3/15));
> > dy1 = zeros(size(x0));
>
> > dy2 = -4*sin(y0*(pi/4/15));
> > dz2 = -4*cos(y0*(pi/4/15));
> > dx2 = zeros(size(x0));
>
> > xfinal = x0 + dx1 + dx2;
> > yfinal = y0 + dy1 + dy2;
> > zfinal = z0 + dz1 + dz2;
>
> > surf(xfinal,yfinal,zfinal)
> > camlight right
> > lighting phong
> > shading interp
> > box on
> > grid on
>
> > I'll let you figure out the proper set of
> > parameters.
>
> > John
>
> What I have done is this
> angle=25;
> x = angle*(-pi/180):0.1:angle*(pi/180); y = angle*(-pi/180):
> 0.1:angle*(pi/180);
> [xIndex, yIndex] = meshgrid(x, y);
> v = sqrt(xIndex.^2 + yIndex.^2);
> surf(cos(v))
> Now I need to run cos(v) not from 32x32 but 40x20 and have the values
> scaled according to it. Such that along x dimension the angle runs
> between 25 degree and along Y with corresponding angle ( will be less
> then 25 degree I believe)
> any suggestions ?

Now I have problem that the grid needs to be of size 40x60 but with
the following code its 41x61. I do not know how to make it 40x60 and
the center value should lie at 20,30 (or what its center to be).
gridx=1/30;gridy=1/20;
x = -1:gridx:1; y = -1:gridy:1;
angle=(38)*(pi/180);
xn=x*angle;yn=y*angle;
[xIndex, yIndex] = meshgrid(xn, yn);
v = sqrt(xIndex.^2 + yIndex.^2);
aa=v(1:40,1:60);
avec=cos(aa(:));

fas <faisalmufti@gmail.com> wrote in message <a6310ebf-4489-4a53-8bc4-
5427712c1683@w5g2000prd.googlegroups.com>...

> Now I have problem that the grid needs to be of size 40x60 but with
> the following code its 41x61. I do not know how to make it 40x60 and
> the center value should lie at 20,30 (or what its center to be).
> gridx=1/30;gridy=1/20;
> x = -1:gridx:1; y = -1:gridy:1;
> angle=(38)*(pi/180);
> xn=x*angle;yn=y*angle;
> [xIndex, yIndex] = meshgrid(xn, yn);
> v = sqrt(xIndex.^2 + yIndex.^2);
> aa=v(1:40,1:60);
> avec=cos(aa(:));

Use linspace instead of the expressions

-1:gridx:1

John

On May 29, 7:23 pm, "John D'Errico" <woodch...@rochester.rr.com>
wrote:
> fas <faisalmu...@gmail.com> wrote in message <a6310ebf-4489-4a53-8bc4-
>
> 5427712c1...@w5g2000prd.googlegroups.com>...
>
> > Now I have problem that the grid needs to be of size 40x60 but with
> > the following code its 41x61. I do not know how to make it 40x60 and
> > the center value should lie at 20,30 (or what its center to be).
> > gridx=1/30;gridy=1/20;
> > x = -1:gridx:1; y = -1:gridy:1;
> > angle=(38)*(pi/180);
> > xn=x*angle;yn=y*angle;
> > [xIndex, yIndex] = meshgrid(xn, yn);
> > v = sqrt(xIndex.^2 + yIndex.^2);
> > aa=v(1:40,1:60);
> > avec=cos(aa(:));
>
> Use linspace instead of the expressions
>
> -1:gridx:1
>
> John

Thank you!